Polenta Fingers With Beans and Tomatoes with seasoning

7 1/2 cups milk , and water, mixed (3 pints) 2 teaspoons salt 1 1/2 cups polenta (10 oz) 2 tablespoons butter , plus extra for spreading 2 ounces parmesan[...]

2 tablespoons unsalted butter , plus extra for the baking dish 2 cups polenta or 2 cups coarsely ground yellow cornmeal 1 quart water or 1 quart chicken stock[...]